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PART THREE A CONCRETE CEMENT Manufacturing company produces HOLLOW BLOCKS and uses three processes in the production. The process requires different amounts of labor, Cement and Gravel. Aside from the HOLLOW BLOCKS, BRICKS is a side product but which has limited demand in the market. The Data below shows the result of 1 Hour operation of each process: INPUT CEMENT (lb) 400 280 600 LABOR (Hours) 16 22 14 PROCESS 1 PROCESS 2 PROCESS 3 OUTPUT HOLLOW BLOCKS (lb) 1100 1470 1200 GRAVEL (lb) 290 240 450 BRICKS (lb) 70 30 150 For a week's production, the company has up to 10 tons of CEMENT at $86/ton, 700 hours of LABOR at $31.50/hr and an unlimited supply of GRAVEL at 24/ton. Every hollow block is priced at $1300/ton and a maximum of 1 ton of the brick can be sold at $74(note that any amount of the brick greater than 1 ton has no value). Due to these restrictions, not any of the processes can be employed for more than 80 hours in any week. However, the division manager can request her workers to work up to an extra 40 hrs per week in overtime at a cost of $45/hr to the firm. The plant vice president in charge of production wants to generate an operating schedule that maximizes the net income. Moreover, he wants to know if the division can meet its weekly production requirements with the material on hand without using overtime and, if so, the minimal cost of this operation. And, because the decision to allow overtime must be made at the plant level, the vice-president also wants some estimate on how much money, if any, the division can save by using overtime